She bought two 1/5-page ads, nine 1/20-page ads, and five 1/4-page ads. What is the total amount of space she bought?

Question

A new resturaunt owner purchased ads to be put in the paper over several days. She bought two 1/5-page ads, nine 1/20-page ads, and five 1/4-page ads. What is the total amount of space she bought?

Answer 1

Since multiplying and addition fractions is known to be inherently difficult, I'll break it down into steps:

Step 1) Let's start by creating an algebraic expression of the word question:

We want the total, so this is = 2 * 1/5 + 9 * 1/20 + 5 * 1/4

 

Step 2) Adding fractions is easier if we find the common denominator:

2 * 1/5 + 9 * 1/20 + 5 * 1/4

So lets look at the denominators of the fractions we are dealing with.

We have 5, 20, and 4.

All of these numbers 5, and 4, and 20 go into 20 at least 1 times, so we can use 20 as our common denominator.

 

Step 3) Next we convert each fraction to have a denominator of 20:

Lets fix the each fraction:

1/5: 5 goes into 20 4 times, so we multiply top and bottom of fraction with 4.

and we get 4/20

1/20: 20 goes into 20 1 times, so we multiply top and bottom of fraction with 1.
and we get 1/20

1/4: 4 goes into 20 5 times, so we multiply top and bottom of fraction with 5.
and we get 5/20

 

Step 4) So our original expression: 2 * 1/5 + 9 * 1/20 + 5 * 1/4

now becomes 2 * 4/20 + 9 * 1/20 + 5 * 5/20

 

Step 5) Evaluate

evaluate top numbers to get 8/20 + 9/20 + 25/20 

now that we have the same denominator for all, we can just add the top numbers and keep the same denominator

we get (8+9+25)/20  = 42/20 = 2.1

The total amount of space she bought is 2.1 ads

Step 6) Check your work.

Let's check our work with a calculator: 2 * 1/5 + 9 * 1/20 + 5 * 1/4 = 0.4 + 0.45 + 1.25 = 2.1 ads

 

Answer 2

2(1/5) + 9(1/20) + 5(1/4)

 2/5     +   9/20   +   5/4         [just multiplying to get fraction totals]

  8/20   +  9/20    +  25/20     

   [the common denominator is 20, so change fractions so we can add numerators]

 (8 + 9 + 25) / 20

    42/20       [this is an improper fraction, so change it to a mixed number]

      2  2/20

      2  1/10 pages         [reduce the fraction]